Ways to get better at physics.

I consider myself good with numbers; computations and stuff. But when it comes to the conceptual analysis of physics, this is the area where I cringe. Right now I am taking calculus-based E&M (I want to be an engineer), I am having trouble understanding visualizing concepts like Faraday's Law motional EMF( changing magnetic field, induced current), RL circuits, and other similar topics.

I am not sure if I should even go into engineering. I do enjoy taking physics, but even I study a lot I don't seem to do well on exams.

I guess my problem is when I am working on a problem, most of the times I just look for the appropriate formula and try to come up with a solution, never really go deep into the conceptual analysis of the problem.

The best way to get better is to practice. Of course, this is probably obvious to you.

It sounds like you try to rush through problems. Is this correct? If so, this is definitely a poor approach to solving problems. Each step in the problem-solving process is just as important as deriving the final answer; each should be checked and verified.

I would like to provide more feedback, but need more info from you. How is your understanding of introductory calculus-based physics? You didn't mention it, so did your troubles start with E&M? How do you actually approach the content knowledge? For example, do you just "read" the text and then try to solve problems, or do you actually go through the derivations and practice examples yourself?

When I think I do know how to solve a particular problem, but when I am present another with similar concept, but maybe different context (like finding magnetic field on an infinite straight wire, if someone show me how to do it, then I am fine. But if I am present with a similar problem but this time on a solenoid, then I wouldn't know how to approach).

Well, you probably learned the fact that solving physics problems isn't a plug-and-chug process. Some beginning students tend to have this misconception.

I didn't get as detailed as a response from you as I would have liked, so here are a few more general ideas. My previous post implied some ideas to improve your understanding if your not already doing them. There are many books on E&M, so it may be worth your time and money to get a different perspective from a different author. You can easily find worked out examples on the internet. There are many good books that teach one how to think when it comes solving mathematical and physics problems. For this avenue, I highly recommend "How to Solve It" by Polya. Although its main focus is in solving mathematical problems, it carries over well to physics problems.

As for your given example, the simplest concept would be to use Amperian loops to solve the problem. Since you didn't have success by yourself and now that you know the answer, you can try deriving the same result using the Biot-Savart Law, which is a more difficult approach. It tends to be easier to solve a problem when you know what the final goal (answer) already is.